# %pip install -q dimstack
import plotly
plotly.offline.init_notebook_mode()
# disable logging
import logging
logging.getLogger().disabled = True
import dimstack as ds
import numpy as np
ds.display.mode("df")
m1 = ds.BasicDimension(
nom=2.565/2,
tol=ds.tol.SymmetricBilateral(0.05/2),
name="Datum C Slot Size",
)
m2 = ds.BasicDimension(
nom=0.7/2,
tol=ds.tol.SymmetricBilateral(0.07/2),
name="Datum C Slot Length",
)
m3 = ds.BasicDimension(
nom=-np.sqrt(45.05**2 + 39.8**2),
# tol=ds.tol.SymmetricBilateral(np.sqrt(0.3**2 + 0.27**2)),
tol=ds.tol.SymmetricBilateral(np.sqrt(0.46**2 + 0.4**2)),
name="Datum C Slot Location",
desc="Relative to Datum B",
)
m4 = ds.BasicDimension(
nom=3.065/2,
tol=ds.tol.SymmetricBilateral(0.05/2),
name="Datum B Hole Size",
)
m5 = ds.BasicDimension(
nom=-2.99/2,
tol=ds.tol.SymmetricBilateral(0.03/2),
name="Datum B Pin Size",
)
m6 = ds.BasicDimension(
nom=np.sqrt(45.05**2 + 39.8**2),
tol=ds.tol.SymmetricBilateral(0.08/2),
name="Datum C Pin Position",
desc="Relative to Datum B Pin",
)
m7 = ds.BasicDimension(
nom=-2.49/2,
tol=ds.tol.SymmetricBilateral(0.03/2),
name="Datum C Pin Size",
)
items = [m1, m2, m3, m4, m5, m6, m7]
stack = ds.Stack(title="Datum C Pin-Slot Gap", items=items)
stack
| ID | Name | Description | dir | Nom. | Tol. | Sen. | Relative Bounds | Distribution | Process Sigma | k | C_p | C_pk | μ | σ | μ_eff | σ_eff | Yield Probability | Reject PPM |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 344 | Datum C Slot Size | Dimension | + | 1.2825 | ± 0.025 | 1 | [1.2575, 1.3075] | Uniform | ||||||||||
| 345 | Datum C Slot Length | Dimension | + | 0.35 | ± 0.035 | 1 | [0.315, 0.385] | Uniform | ||||||||||
| 346 | Datum C Slot Location | Relative to Datum B | - | 60.11275 | ± 0.60959 | 1 | [59.50316, 60.72234] | Uniform | ||||||||||
| 347 | Datum B Hole Size | Dimension | + | 1.5325 | ± 0.025 | 1 | [1.5075, 1.5575] | Uniform | ||||||||||
| 348 | Datum B Pin Size | Dimension | - | 1.495 | ± 0.015 | 1 | [1.48, 1.51] | Uniform | ||||||||||
| 349 | Datum C Pin Position | Relative to Datum B Pin | + | 60.11275 | ± 0.04 | 1 | [60.07275, 60.15275] | Uniform | ||||||||||
| 350 | Datum C Pin Size | Dimension | - | 1.245 | ± 0.015 | 1 | [1.23, 1.26] | Uniform |
ds.plot.StackPlot().add(stack).show()
display(stack.WC)
| ID | Name | Description | dir | Nom. | Tol. | Sen. | Relative Bounds | Distribution |
|---|---|---|---|---|---|---|---|---|
| 392 | Datum C Pin-Slot Gap - WC Analysis | + | 0.425 | ± 0.76459 | 1 | [-0.33959, 1.18959] | Uniform |
Since the left side of the slot is our 0 point, we want the left size of the pin to be in the positive direction, or the bounds of the entire tolerance stack to be greater than zero.
At worst-case, the lower bound is negative, meaning the pin would not fit in the slot.
What if we don't need it to fit every time, just pretty dang close to almost every time...
display(stack.RSS)
display(stack.SixSigma(at=1))
display(stack.SixSigma(at=2))
display(stack.SixSigma(at=4.5))
| ID | Name | Description | dir | Nom. | Tol. | Sen. | Relative Bounds | Distribution | Process Sigma | k | C_p | C_pk | μ | σ | μ_eff | σ_eff | Yield Probability | Reject PPM |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 520 | Datum C Pin-Slot Gap - RSS Analysis | (assuming inputs with Normal Distribution & ± 3σ) | + | 0.425 | ± 0.61329 | 1 | [-0.18829, 1.03829] | Normal | ± 3σ | 0 | 1.0 | 1.0 | 0.425 | 0.20443 | 0.425 | 0.20443 | 99.73002039 | 2699.8 |
| ID | Name | Description | dir | Nom. | Tol. | Sen. | Relative Bounds | Distribution | Process Sigma | k | C_p | C_pk | μ | σ | μ_eff | σ_eff | Yield Probability | Reject PPM |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 528 | Datum C Pin-Slot Gap - '6 Sigma' Analysis | (assuming inputs with Normal Distribution) | + | 0.425 | ± 0.20443 | 1 | [0.22057, 0.62943] | Normal | ± 1σ | 0 | 0.33333 | 0.33333 | 0.425 | 0.20443 | 0.425 | 0.20443 | 68.26894921 | 317310.51 |
| ID | Name | Description | dir | Nom. | Tol. | Sen. | Relative Bounds | Distribution | Process Sigma | k | C_p | C_pk | μ | σ | μ_eff | σ_eff | Yield Probability | Reject PPM |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 536 | Datum C Pin-Slot Gap - '6 Sigma' Analysis | (assuming inputs with Normal Distribution) | + | 0.425 | ± 0.40886 | 1 | [0.01614, 0.83386] | Normal | ± 2σ | 0 | 0.66667 | 0.66667 | 0.425 | 0.20443 | 0.425 | 0.20443 | 95.44997361 | 45500.26 |
| ID | Name | Description | dir | Nom. | Tol. | Sen. | Relative Bounds | Distribution | Process Sigma | k | C_p | C_pk | μ | σ | μ_eff | σ_eff | Yield Probability | Reject PPM |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 544 | Datum C Pin-Slot Gap - '6 Sigma' Analysis | (assuming inputs with Normal Distribution) | + | 0.425 | ± 0.91994 | 1 | [-0.49494, 1.34494] | Normal | ± 4.5σ | 0 | 1.5 | 1.5 | 0.425 | 0.20443 | 0.425 | 0.20443 | 99.99932047 | 6.8 |
Let say we design the slot to +/-1sigma, the part has a (100%-68%=) 32% chance of not being able to fit in the mounting hardware. Thats not very good. But the bound is pretty far from our limits (limit > 0).
If look at +/-2sigma, the lower bounds is barely in the positive region, this is our process capability. Therefore, the current slot length will only fit 95% of the time.
If we wanted to target W.C, RSS, +/-3sigma, or +/-4.5sigma, we would have to rework the dimensions to keep the bounds within the positive region for those capabilities
spec = ds.Spec("stack spec", "", dim=stack.SixSigma(at=2), LL=0.0, UL=99)
spec
| Name | Description | Dimension | Spec. Limits | Median | k | C_p | C_pk | Yield Probability | Reject PPM |
|---|---|---|---|---|---|---|---|---|---|
| stack spec | 512: Datum C Pin-Slot Gap - '6 Sigma' Analysis (assuming inputs with Normal Distribution) +0.425 ± 0.40886 @ ± 2σ & k=0 | [0.0, 99] | 49.5 | 0.99141 | 80.71218 | 0.69298 | 100 | 0 |